Opposite of extrude (removing)
There are several ways to do this.  The two that I think are most straightforward are:


Subdivide the 4 edges that are coaxial with the direction you want to "shrink" the mesh in.  Slide the verts along the existing edges to where you want them to be and connect them by subdividing (knife tool) the existing faces.  You can then delete the faces that stick out (there should be 5 of them) and create a new face using the new vertices.
Boolean operations.  I'm not exactly sure why this isn't working for you, but I have a few guesses.  First, both objects you're using have boolean operations configured, but not applied.  You may need to apply the boolean to the first object ('stand') before it can be used on another object ('Astand').  Second, it looks like the faces of your objects are coplanar, causing a well known problem commonly known as Z-fighting.  This should be resolved before applying any boolean operations.  Finally, it can be hard to tell if a boolean operation applied successfully when all the objects are still visible.  I'd turn off the visibility of the object you're subtracting ('stand') while leaving the object you're subtracting it from ('Astand') visible.